Fixed points of left reversible semigroup of isometry mappings in Banach spaces

TL;DR

This paper proves the existence of common fixed points for left reversible semigroups of isometry mappings in Banach spaces, specifically in the Chebyshev center, extending previous results in the field.

Contribution

It introduces new fixed point existence results for semigroups of isometries in Banach spaces, improving upon earlier findings by Lim et al. and Brodskii and Milman.

Findings

Existence of common fixed points in Chebyshev centers.

Improved fixed point results over previous studies.

Applicable to left reversible semigroups of isometries.

Abstract

In this paper, we prove the existence of a common fixed point in $C(K)$, the Chebyshev center of K, for a left reversible semigroup of isometry mappings. This existence result improves the results obtained by Lim et al. and Brodskii and Milman.